What is the Elastic Contraction of a Propeller Shaft at Full Power?

[Chacabucogod]

A propeller shaft in the largest and most powerful ships transmits about 50,000 hp (1HP=33,000 ft*lb/min). Assume that the propeller transforms this power into a forward push on the ship with an efficiency of 70 per cent and that the ship's speed then is 30 knots (1 knot is 6,080 ft/hr).
The shaft is 300 ft long from the propeller to the thrust bearing in the engine room, where the thrust is transmitted to the ship's hull structure. The diameter of the (solid, circular) shaft is 24 in. Calculate the elastic contraction of the shaft at full power. (Answer:0.985 in).

There is no number for E provieded. So I assumed it's 30,000,000 lb/in^2. Maybe that's where the problem lies.

Homework Equations

$$\Delta l=\frac{FL}{EA}$$
$$Power=F*v$$
Power=$1.65x10^9 \frac{ft*lb}{min}$
$speed=182,400\frac{ft}{hr}$$$50,000*33,000*0.7=v*182,400*\frac{1 hour}{60 min}$$
F=379.934x10^3 lb
$$\frac{379.934x10^3*300*12}{144\pi *30,000,000}$$
Ans=0.105 in

 

[SteamKing]

Propeller shafts are made of steel, so using E = 30*10^6 psi is OK.

I think the problem's given answer is suspect, maybe a misprint (0.0985 in instead of 0.985 in). I found no problems with your formulas or arithmetic.

 

[Doug Huffman]

There is a complex stress in torsion that causes Euler strain and fractures as I recall from a long time ago. The demonstration was of the 45° angles in a twisted piece of chalk.

A practical propellor shaft of those dimensions would be hollow and filled with an incompressible (in my case, sand).